Terahertz radiation bridges the gap between the microwave and optical regimes. It has unique properties such as fingerprint characteristics, non-destructive testing and transparency to various materials, which makes terahertz waves have significant scientific and technological potential in drug testing applications. Terahertz time-domain spectroscopy plays an important role in identifying target drugs containing absorption peaks. It can be used to discriminate specific molecules contained in drugs or the changes of components in samples, as many molecules have characteristic absorption peaks in the terahertz regime. Thus, to solve the problems of identifying weak absorption peaks of low content targets in the mixture, in this paper, the adjoint inflection point (AIP) method based on the discrete local maximum (DLM) method is proposed for identifying the characteristic absorption peaks in terahertz regime for the effective identification of the low content target. Firstly, the adjoint inflection points of potential absorption peaks are obtained using the first and second derivative of the terahertz absorption coefficient spectrum. Secondly, the difference spectrum is calculated by performing the operation between the original absorption spectrum and the baseline spectrum. At last, the absorption peak positions are determined by using the DLM method along the difference spectrum. Also, this AIP method is applied to the absorption peak extraction of four nitrofurans sample spectra. The result is compared with the peak positions determined by DLM, and the peak positions are also compared with the peaks calculated by the density functional theory. The better performance of the recognition capacity of the AIP method is observed and verified, especially for weak absorption peaks. This method suggests that it has profound application potential in spectroscopic analyses and even in determining curve peaks in various applications.